Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×D7×D8 |
| Fitting | C5×C7×D8 ⋊ C2 |
| Hall | C5×C7 ⋊ C2×D8 |
| Sylow | C7 ⋊ C2×C5×D8 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D8×AGL(1,𝔽7), D5×D7×D8, C5×D7×AGL(1,ℤ/8), … |
| maximal normal subgroup of | C5×D8×AGL(1,𝔽7), D5×D7×D8, C5×D7×AGL(1,ℤ/8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 674);